MoeaBench v0.8.0 Technical Calibration Report

1. Methodology & Experimental Context

This report serves as the official scientific audit for MoeaBench v0.8.0. The objective is to validate and calibrate the numerical integrity and topological fidelity of the framework's core algorithms against established mathematical benchmarks (Ground Truth).

Experimental Setup

• Population Framework: All algorithms used a population size of N=200.
• Evolutionary Budget: Runs were executed for exactly 1000 generations.
• Statistical Baseline: Metrics in the summary tables are derived from 30 independent runs to ensure stochastical significance.
• Objective Space: All problems were configured with M=3 objectives for volumetric analysis.
• Normalization Strategy: We enforce Strict Theoretical Normalization. The [0, 1] range is mapped exclusively from the theoretical Ideal and Nadir points of the Ground Truth, not from observed data.

2. Metric Glossary & Interpretation

• IGD (Inverted Generational Distance): Measures both convergence (proximity) and diversity (spread). Lower is strictly better.
• EMD (Uniform): Earth Mover's Distance against a uniformized GT reference. Certification uses EMD_eff (ratio to calibrated floor for the same K), not a fixed absolute cutoff.
• Purity (GD_p95): 95th-percentile distance from population to GT. Certification uses Purity_eff (ratio to calibrated floor).
• H_raw: The absolute hypervolume calculated with Reference Point 1.1.
• H_ratio: $H_{raw} / RefBox$. Search area coverage (volume). Strictly $\le 1.0$.
• H_rel: $H_{raw} / H_{GT}$. Convergence to optimal front. Can exceed 100% due to saturation.

3. Clinical Quality Matrix: Interpretation

• FIT: Measures the proximity of the population to the mathematical surface. High quality (near 1.0) indicates that points are exactly on the front.
• COVERAGE: Evaluates the global spread. High quality indicates the algorithm found the entire extent of the Pareto front without skipping regions.
• DENSITY ($Q_{density}$): Inverse of the largest gap size ($IGD_{95}$). High quality assures the front is densely populated without significant interruptions in the manifold.
• REGULARITY ($Q_{reg}$): Inverse of the Wasserstein distance to a theoretical uniform lattice. High quality indicates equidistant spacing between solutions.
• BALANCE ($Q_{bal}$): Inverse of the Jensen-Shannon divergence from the ideal cluster distribution. High quality guarantees unbiased coverage across all trade-off regions.

3.1. Numerical Definition & Certification

The Quality Score $Q$ is calculated by normalizing raw metrics against two strict baselines: the Optimal Uniform Sampling ($U_{ref}$) and a Random Sampling ($R_{ref}$) of the Ground Truth.

Certification Terciles: The final verdict is determined by the minimum quality across all 5 dimensions (Weakest Link Principle).

• RESEARCH TIER ($Q_{min} \ge 0.67$): Algorithm is statistically indistinguishable from the theoretical optimum in all aspects.
• INDUSTRY TIER ($0.34 \le Q_{min} < 0.67$): Algorithm is robust and better than random, but shows measurable deviation from perfection (e.g., slight irregularity).
• FAILURE ($Q_{min} \le 0.33$): Algorithm failed to converge or produced a distribution equivalent to (or worse than) random guessing in at least one dimension.